Find the half-life of uranium, given that `3.32 xx 10^(7) g` radium is found per gram of uranium in old minerals. The atomic weights of uranium and radium are `238` and `226` and half-life of radium is `1600` years (Avogadro number is `6.023 xx 10^(23)//g -"atom"`).

Explanation

To find the half-life of uranium based on the given information, we can follow these steps:

### Step 1: Understanding the Relationship
In old minerals, uranium and radium exist in radioactive equilibrium. This means that the rate of disintegration of uranium equals the rate of formation of radium. Mathematically, we can express this as:

\[ \lambda_U N_U = \lambda_R N_R \]
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